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Meyers' boundary regularity conjecture for weak lower semicontinuity
Meyers' conjecture. Condition (ii) can be dropped if $\partial\Omega$ is smooth enough or if a smooth enough function is prescribed on the boundary as the datum.
Conjectureopenboundary-regularity calculus-of-variations weak-lower-semicontinuityarXiv posted 2 days ago

Meyers' boundary regularity conjecture for weak lower semicontinuity